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Potential non-relativistic QCD provides a convenient framework to study the three heavy-quark system. We have studied its symmetries under exchange of the heavy quarks and determined the leading ultrasoft contributions to the singlet static potential and to the singlet static energy. Specializing to an equilateral geometry, we have solved the renormalization group equations in order to resum the leading ultrasoft logarithms for the singlet static potential, which is thus known at NNLL accuracy.

The Symmetries of the Three Heavy Quark Bound State and the Singlet Static Energy